We study the differential equation ẍ(t) = a(t)V '(x(t)), where V is a double-well potential with minima at x = ±1 and a(t) →l > 0 as |t| → 1. It is proven that under certain additional assumptions on a, there exists a heteroclinic solution x to the differential equation with x(t) → -1 as t → -1 and x(t) → 1 as t → ∞. The assumptions allow l - a(t) to change sign for arbitrarily large values of |t|, and do not restrict the decay rate of |l -a(t)| as |t| → ∞ © 2010 Texas State University - San Marcos.
Electronic Journal of Differential Equations
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Scholarly Commons Citation
Spradlin, G. S. (2010). Heteroclinic Solutions to an Asymptotically Autonomous Second-Order Equation. Electronic Journal of Differential Equations, 2010(137). Retrieved from https://commons.erau.edu/db-mathematics/1